You'll have to get rid of that spike. That spike can cause a glitch in the audio stream or even a dropout. Some laptops cannot be fixed. My son bought a Dell Studio , cost him $1,400 and he's a very highly qualified computer tech, He could not get rid of the latency spikes. He even sent it back to Dell but they had no clue and to them the machine worked 100%.
He ended up purchasing a $500 Acer that had no issues once tweaked.
With mine it was the battery management which you disable in the device manager. But there are other things that an OS can busy it self with causing the spikes.
The Tascam will record all 16 inputs but you need a digital source for channel 15/16 SPDIF. It gets tricky with word clock so I do not use it when multi tracking.
It is very true regarding your USB ports as well. I always use the same port and I do not plug any other USB devices in while recording. I use the touch pad.
Sounds like you may have to look into a better laptop if this one has those issues.
Don't tell anyone I suggested this: Record @ 24/48 then up convert the file before handing it back to the client. Dare anyone to claim it was not recorded otherwise. ( did I just say that? no,, couldn't have been me, must have been someone else.)